solns21b-ps1-Jan11

solns21b-ps1-Jan11 - Chemistry 21b Problem set # 1 Out: 05...

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Chemistry 21b Problem set # 1 Out: 05 January 2011 Due: 12 January 2011 Please note the following: (a) Completed assignments should be turned in NO LATER THAN 5 PM to either the appropriate TA’s or the instructor’s mailboxes on the due date. You will lose 20% of your actual grade for everyday for which your assignment is late. After Fve days your assignment would still be graded but you will receive no credit. So, please discuss any need for an extension with one of us in advance, and remember that 1/3 of your Fnal grade will be based on these assignments. Problems are worth: 1=30, 2=30, 3=40. (b) Collaboration is permitted within the guidelines posted on the Ch21b Problem Sets page, but please try and use your own words when you are explaining your solutions. Don’t hesitate to contact us if you Fnd ambiguities. Corrections or clariFcations will be posted to the Ch21b web pages, as will the solution sets once all the assignments are turned in and graded. (c) So that we can get an idea of how much time you are spending on these problems, please note on the Frst sheet of your assignment how many hours you spent working on each assignment. lots of equations, etc. in your answers you’ve probably missed some simplifying principle. .. 1. Problem 9.28. McQuarrie, page 492 (prove that the Slater determinant wavefunction outlined by eq. (9.51), page 453, when used to calculate the energy of an atom with 2N electrons, produces eq. (9.53), whose terms are illustrated in eq. (9.54-9.56). 2. Problem 9.34. McQuarrie, pages 493-494 (caclulations demonstrating that ±igure 9.6 and eq. (9.74), page 461, are correct). 3. Give the spectroscopic terms arising from the following conFgurations, using LS coupling. Include the J values that are appropriate. a) 3p 4s b) 4d 5d c) 3d 2 (Hint: only Fve terms of those found under b) remain, you can use the microstates/Slater determinant approach outlined in § 9.10 to Fgure out which remain.) d) 3p 4 4s (you can use the results for equivalent p electrons outlined in § 9.10) e) 2p 2 4p (you can use the results for equivalent p electrons outlined in § 9.10) f) 3p 3 (Hint: only three terms of those found under e) remain. Give arguments of the three that are likely to remain, rather than writing out completely all the possible Slater determinants.) Responsible TA for Problem Set #1: Jason Crowley ([email protected])
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486 Chapter 9 However, only the first 1/ ! terms in the square of the wave function yieid non-zero integrals, each of which equals one when integrated over all the electron coordinates, due to the normalization of the individual Slater spin orbitals. Ai1 the cross products yieid a zero integral because of the orthogonality of at least one spin orbital. Thus. the integration of the square of the N x .V Slater determinant of spin orbitals over all space results in a vahre of N!. Therefore. the normalization constant for the Slater determinant is I,
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This note was uploaded on 01/03/2012 for the course CH 21b taught by Professor List during the Fall '10 term at Caltech.

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solns21b-ps1-Jan11 - Chemistry 21b Problem set # 1 Out: 05...

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